In this dissertation work, I investigate the decoherence time of a Josephson vortex qubit (JVQ) and the level of entanglement between two JVQs. A JVQ may be fabricated by embedding two closely spaced microresistors in the insulating layer of a long Josephson junction (LJJ). The phase dynamics of the JVQ may be described by using the perturbed sine-Gordon equation. This sine-Gordon equation is transformed to describe the motion of fluxons in the double-well potential. An oscillation of a fluxon in this double-well potential is mapped onto a quantum two-state system. The coherent oscillation of fluxons in the two-state system decays due to dissipation and noises in the LJJ. To estimate the decoherence time, the two-state system in a noisy environment is described by using the spin-boson Hamiltonian. The time evolution of the system is studied by using the generalized master equation. Finally, I use the experimental parameters for Nb-AlOx-Nb Josephson junction to estimate the decoherence time. The result shows that JVQ has a very long decoherence time (several tens of microseconds) compared to other Josephson qubits. Entanglement between two coupled JVQs is estimated by computing the concurrence. The concurrence depends on the ground-state energy splitting due to the one-fluxon and two-fluxon tunneling between the potential minima of the two coupled JVQs. The tunneling amplitude between the potential minima depends on the junction parameters such as magnetic induction effect S, the separation distance ℓ, and the pinning strength of the microresistors ϵ. The estimation of the concurrence shows that a near perfect entanglement may be achieved by using the experimentally accessible values of the parameters. Also the study shows that the tunneling amplitude of the fluxon between the potential minima of the JVQs may be increased by coupling the junction with a resonant cavity. This characteristic of the junction-cavity coupling may be exploited to control the entanglement between two JVQs.